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The Haberdashers’ Aske’s Boys’ School Elstree, Herts

11+ Entrance Examination 2011

MATHEMATICS Time : One Hour

Full Name

...........................................................

Candidate Number

......................................

Please follow these instructions

•

Do not open this paper until you are told to do so.

•

There are 30 questions on this paper. Do not forget to turn over.

•

Work quickly but accurately. You are recommended to use pencil, but you can use pen or biro if you wish.

WRITE YOUR ANSWERS TO THE QUESTIONS IN THE SPACES PROVIDED. YOU MAY USE THE SPACE AT THE BOTTOM OF EACH PAGE FOR WORKING. Answer 1.

Add:

48 + 27

_______

2.

Subtract:

91 − 25

_______

3.

Multiply:

62 × 7

_______

4.

Divide:

92 ÷ 4

_______

5.

I have £8.17 credit on my mobile phone. At the end of a phone call this falls to £7.65. How much did the call cost?

_______

The drink “Raspberry Heaven” is 1 part raspberry juice, 2 parts orange juice and 3 parts apple juice. How much raspberry juice does a 300 ml glass of Raspberry Heaven contain?

_______

6.

7.

Work out the product of 528 and 99.

8.

Barbie earns £23,450 a year and her partner Ken earns £700 less than Barbie. How much do the couple earn altogether?

_______________

9.

Convert 7.4 kilograms into grams.

10.

Arrange the following numbers in order of size starting with the smallest: 32.043, 0.099, 1.072, 0.491, 0.5

__________ _________

_______________________________________________________________ 11.

The opening hours of my local supermarket are 7am to 9pm Mondays to Saturdays and 10:30am to 4:30pm on Sundays. For how many hours does this supermarket open each week? __________

12.

Arrange the numbers, 5, 3, 7 and 2 to make the largest possible four-digit number which is a multiple of 5.

_________

Work out 0.08 multiplied by 5.

_________

13.

SPACE FOR WORKING

Answer 14.

The new TV channel, Lazy Living, broadcasts for 98 hours a week. If two-sevenths of its output is devoted to make-over programmes and the rest to celebrity gossip, for how many hours each week does the channel broadcast programmes on celebrity gossip? _________

15.

For breakfast I eat a slice of buttered toast and a cup of coffee. The time taken to complete these activities is as follows: Brown toast in toaster Butter the toast Make coffee in machine

3 minutes 1 minute 2 minutes

Jonathan thinks that the shortest time taken for me to prepare my breakfast is 6 minutes. Explain briefly why Jonathan is wrong. ________________________________________________________________ What is the correct shortest time? 16.

________

The chart below shows the mileage between five places in North London. For example it gives the distance between Kenton and Hampstead as 4 miles. ON

T EN

K

N DE

N PE AR

19

H

11

18

SO

4

20

8

5

13

9

E

AT HG T U

D

EA ST P M HA 10

BS HA

Daisy lives in Hampstead and drives her son to school at Haberdashers’ in the morning before continuing on to the office in Southgate. She then visits her sister in Harpenden before driving home via Habs. How far does she travel altogether? _________ SPACE FOR WORKING

Answer 17. The rate of VAT (value-added tax) in this country is 20%. In the shop CoCost, the price of a TV excluding VAT is £550. Work out the cost of the TV after the VAT is added on.

________

The price of a diamond ring, including VAT is £1200. Work out the cost of the ring before the VAT was added on.

________

18. Train A leaves Birmingham New Street station at 1747 travelling due North on the slow line at 90 km/hour. How many kilometres has this train travelled when the time is 1817? ____________ Train B leaves Birmingham New Street station at 1817 also travelling due North but on the fast line. The speed of train B is 135 km/hour. At what time does train B overtake train A?

_____________

19. The diagram below shows a piece of abstract art hanging up on Andrew’s bedroom wall. To make this look even more interesting he decides to rotate this painting through 90 degrees clockwise. In the space provided show what the painting will look like in its new position.

SPACE FOR WORKING

Answer 20. Every evening Diana has a bath. She turns on the taps and waits patiently for the bath to fill before she turns them off and steps in. At the end of her bath she steps out of the water before pulling out the plug to empty the bath. A graph of the volume of water (measured in litres) plotted against time (measured in minutes) is shown below. Volume of water in litres 1000

750

500

250

0

5

10

20

15

How long does she spend in the bath?

25

30

Time in minutes

__________

Work out the number of litres of water that flow into the bath per minute as the bath fills up. __________ Does the bath empty at a faster, slower or the same rate as it fills? Faster, slower or same? _______________ SPACE FOR WORKING

Answer 21.

Amar (form captain), Brian (vice captain), Charles and Daniel are best friends in the same class at school. They always like to stand next to each other in the lunch queue. On Mondays it is a school rule that the form captain is at the front of the queue followed by the vice captain. There are two ways in which these boys can queue up on a Monday: ABCD and ABDC. On Tuesdays, the form captain must again queue up first but the remaining three boys can follow in any order. There are six ways in which these boys can queue up on a Tuesday. Four of these ways are listed below. Write down the remaining two: ABCD, ABDC, ACBD, ACDB, _______, _________ On Wednesdays there are no restrictions and all four boys can queue up together in any order. In how many ways can this be done? ____________

22.

Isolde enjoys making cubes. She first draws out shapes on pieces of cardboard and then folds them along the lines to form a cube. The diagrams below show six attempts. Unfortunately only five of these actually work. Cross out the shape which is impossible.

SPACE FOR WORKING

23.

As part of a mathematics project a class is asked to look up the lengths of objects on the internet. These objects are listed in the rectangles below and the measurements are given in the triangles. Unfortunately these objects and measurements have been muddled up. Draw lines on the diagram to match each object with its correct length.

Width of Wembley Stadium pitch

Height of an average man

Distance from London to New York

Length of a piece of standard A4 paper

Height of the London Eye

Height of Mount Everest

SPACE FOR WORKING

300 mm

5600 km

135 m

1750 mm

8800 m

6900 cm

Answer 24.

In this question you may assume the following exchange rates: 1 British pound (£) = 1.5 American dollars (US$) 1 British pound (£) = 2 New Zealand dollars (NZ$) The price of a hoodie in the London branch of Abergavenny and Filtch is £80. In New York the price is US$90. How much do I save by buying the hoodie in New York? Give your answer both in US dollars and pounds. Saving = US$ ___________ and £ ___________ My friend Sheila lives in Auckland, New Zealand. She saves US$60 if she buys this hoodie in New York. How much does it cost in New Zealand? Give your answer in New Zealand dollars. NZ$ ___________ Work out the exchange rate for converting New Zealand dollars into American dollars: 1 New Zealand dollar (NZ$) = ______ American dollars (US$) 25. Seven children, A, B, C, D, E, F, G take part in a competition. Use the information below to fill in the table: Position 1st 2nd 3rd 4th 5th 6th 7th § § § § § §

Child

There are no tied positions D beat A C was the winner If you multiply the positions of A and D you get the position of F A and E are in next to each other in the table. B beat G

SPACE FOR WORKING

Answer 26. The average of a set of numbers is worked out by adding the numbers together and then dividing by the number of numbers. Work out the average of: 1, 1, 1

_______

1, 1, 4

_______

1, 4, 7

_______

4, 7, 13

_______

Describe, in words, a simple pattern that you notice about these answers: _______________________________________ Class 6A go on a Geography trip to Eastbourne and investigate the size of pebbles on the beach. Jonnie picks up seven small pebbles and measures their lengths in millimetres. The lengths of the first six pebbles are: 1, 1, 1, 4, 7, 13 Assuming that the pattern that you observed above continues to hold, work out the length of Jonnie’s seventh pebble. ________ 27.

Tristan is given six bags of fruit. Bag A contains 2 apples, 4 oranges and 3 pears. Bag B contains 3 apples, 1 orange and 2 pears. Bag C contains 4 apples, 5 oranges and 3 pears. Bag D contains 4 apples, 6 oranges and 4 pears. Bag E contains 6 apples, 4 oranges and 3 pears Bag F contains 7 apples, 7 oranges and 7 pears. He is allowed to choose one of these bags and then pick just one piece of fruit from that bag at random. Which bag should he choose if he is to maximise his chance of picking an apple? _________ Which bag should he choose if he is to minimise his chance of picking a pear? _________

SPACE FOR WORKING

Answer 28.

The diagram below shows a sequence of squares drawn on a grid. The coordinates of the centre of square number 1 are (1,1). The coordinates of the centre of square number 2 are (2,3). The first number in the pair is the x-coordinate and the second number is the y-coordinate. Write down the coordinates of the centre of square number 3

___________________

square number 4

___________________

square number 10

___________________

square number 234

___________________

The y-coordinate of the centre of one of the squares in this sequence is 2177. Work out the x-coordinate of this square. ________________ y 6

5

3

4

3

2

2

1

1

1

SPACE FOR WORKING

2

3

4

5

6

x

29. In the triangles shown below each number is the sum of the two numbers directly underneath it. For example, 26 = 12 + 14 and 5 = 1 + 4. 26 12 5 1

14 7

4

7 3

4

Complete the triangle of numbers: ____ ____ ____ 1

____ 8

____

7 ____

5

Complete the triangle of numbers: 101 54 ____ 12

SPACE FOR WORKING

____ ____

____

____ 8

____

Answer 30. The diagram below shows a rectangle, 9 units long, 6 units wide and with parts of non-overlapping circles drawn all over it. The circles all have the same radius and the area of each is 7 square units. Work out the shaded area.

9 units

6 units

Shaded area = _________ square units The diagram below shows a square which is 3 units long with four identical semi-circles drawn on each edge. These semi-circles overlap to create four petals which are shaded on the diagram. The area of each semi-circle is 3.5 square units. Work out the shaded area.

3 units

Shaded area =

________ square units

SPACE FOR WORKING

GO BACK AND CHECK YOUR ANSWERS CAREFULLY

View more...
11+ Entrance Examination 2011

MATHEMATICS Time : One Hour

Full Name

...........................................................

Candidate Number

......................................

Please follow these instructions

•

Do not open this paper until you are told to do so.

•

There are 30 questions on this paper. Do not forget to turn over.

•

Work quickly but accurately. You are recommended to use pencil, but you can use pen or biro if you wish.

WRITE YOUR ANSWERS TO THE QUESTIONS IN THE SPACES PROVIDED. YOU MAY USE THE SPACE AT THE BOTTOM OF EACH PAGE FOR WORKING. Answer 1.

Add:

48 + 27

_______

2.

Subtract:

91 − 25

_______

3.

Multiply:

62 × 7

_______

4.

Divide:

92 ÷ 4

_______

5.

I have £8.17 credit on my mobile phone. At the end of a phone call this falls to £7.65. How much did the call cost?

_______

The drink “Raspberry Heaven” is 1 part raspberry juice, 2 parts orange juice and 3 parts apple juice. How much raspberry juice does a 300 ml glass of Raspberry Heaven contain?

_______

6.

7.

Work out the product of 528 and 99.

8.

Barbie earns £23,450 a year and her partner Ken earns £700 less than Barbie. How much do the couple earn altogether?

_______________

9.

Convert 7.4 kilograms into grams.

10.

Arrange the following numbers in order of size starting with the smallest: 32.043, 0.099, 1.072, 0.491, 0.5

__________ _________

_______________________________________________________________ 11.

The opening hours of my local supermarket are 7am to 9pm Mondays to Saturdays and 10:30am to 4:30pm on Sundays. For how many hours does this supermarket open each week? __________

12.

Arrange the numbers, 5, 3, 7 and 2 to make the largest possible four-digit number which is a multiple of 5.

_________

Work out 0.08 multiplied by 5.

_________

13.

SPACE FOR WORKING

Answer 14.

The new TV channel, Lazy Living, broadcasts for 98 hours a week. If two-sevenths of its output is devoted to make-over programmes and the rest to celebrity gossip, for how many hours each week does the channel broadcast programmes on celebrity gossip? _________

15.

For breakfast I eat a slice of buttered toast and a cup of coffee. The time taken to complete these activities is as follows: Brown toast in toaster Butter the toast Make coffee in machine

3 minutes 1 minute 2 minutes

Jonathan thinks that the shortest time taken for me to prepare my breakfast is 6 minutes. Explain briefly why Jonathan is wrong. ________________________________________________________________ What is the correct shortest time? 16.

________

The chart below shows the mileage between five places in North London. For example it gives the distance between Kenton and Hampstead as 4 miles. ON

T EN

K

N DE

N PE AR

19

H

11

18

SO

4

20

8

5

13

9

E

AT HG T U

D

EA ST P M HA 10

BS HA

Daisy lives in Hampstead and drives her son to school at Haberdashers’ in the morning before continuing on to the office in Southgate. She then visits her sister in Harpenden before driving home via Habs. How far does she travel altogether? _________ SPACE FOR WORKING

Answer 17. The rate of VAT (value-added tax) in this country is 20%. In the shop CoCost, the price of a TV excluding VAT is £550. Work out the cost of the TV after the VAT is added on.

________

The price of a diamond ring, including VAT is £1200. Work out the cost of the ring before the VAT was added on.

________

18. Train A leaves Birmingham New Street station at 1747 travelling due North on the slow line at 90 km/hour. How many kilometres has this train travelled when the time is 1817? ____________ Train B leaves Birmingham New Street station at 1817 also travelling due North but on the fast line. The speed of train B is 135 km/hour. At what time does train B overtake train A?

_____________

19. The diagram below shows a piece of abstract art hanging up on Andrew’s bedroom wall. To make this look even more interesting he decides to rotate this painting through 90 degrees clockwise. In the space provided show what the painting will look like in its new position.

SPACE FOR WORKING

Answer 20. Every evening Diana has a bath. She turns on the taps and waits patiently for the bath to fill before she turns them off and steps in. At the end of her bath she steps out of the water before pulling out the plug to empty the bath. A graph of the volume of water (measured in litres) plotted against time (measured in minutes) is shown below. Volume of water in litres 1000

750

500

250

0

5

10

20

15

How long does she spend in the bath?

25

30

Time in minutes

__________

Work out the number of litres of water that flow into the bath per minute as the bath fills up. __________ Does the bath empty at a faster, slower or the same rate as it fills? Faster, slower or same? _______________ SPACE FOR WORKING

Answer 21.

Amar (form captain), Brian (vice captain), Charles and Daniel are best friends in the same class at school. They always like to stand next to each other in the lunch queue. On Mondays it is a school rule that the form captain is at the front of the queue followed by the vice captain. There are two ways in which these boys can queue up on a Monday: ABCD and ABDC. On Tuesdays, the form captain must again queue up first but the remaining three boys can follow in any order. There are six ways in which these boys can queue up on a Tuesday. Four of these ways are listed below. Write down the remaining two: ABCD, ABDC, ACBD, ACDB, _______, _________ On Wednesdays there are no restrictions and all four boys can queue up together in any order. In how many ways can this be done? ____________

22.

Isolde enjoys making cubes. She first draws out shapes on pieces of cardboard and then folds them along the lines to form a cube. The diagrams below show six attempts. Unfortunately only five of these actually work. Cross out the shape which is impossible.

SPACE FOR WORKING

23.

As part of a mathematics project a class is asked to look up the lengths of objects on the internet. These objects are listed in the rectangles below and the measurements are given in the triangles. Unfortunately these objects and measurements have been muddled up. Draw lines on the diagram to match each object with its correct length.

Width of Wembley Stadium pitch

Height of an average man

Distance from London to New York

Length of a piece of standard A4 paper

Height of the London Eye

Height of Mount Everest

SPACE FOR WORKING

300 mm

5600 km

135 m

1750 mm

8800 m

6900 cm

Answer 24.

In this question you may assume the following exchange rates: 1 British pound (£) = 1.5 American dollars (US$) 1 British pound (£) = 2 New Zealand dollars (NZ$) The price of a hoodie in the London branch of Abergavenny and Filtch is £80. In New York the price is US$90. How much do I save by buying the hoodie in New York? Give your answer both in US dollars and pounds. Saving = US$ ___________ and £ ___________ My friend Sheila lives in Auckland, New Zealand. She saves US$60 if she buys this hoodie in New York. How much does it cost in New Zealand? Give your answer in New Zealand dollars. NZ$ ___________ Work out the exchange rate for converting New Zealand dollars into American dollars: 1 New Zealand dollar (NZ$) = ______ American dollars (US$) 25. Seven children, A, B, C, D, E, F, G take part in a competition. Use the information below to fill in the table: Position 1st 2nd 3rd 4th 5th 6th 7th § § § § § §

Child

There are no tied positions D beat A C was the winner If you multiply the positions of A and D you get the position of F A and E are in next to each other in the table. B beat G

SPACE FOR WORKING

Answer 26. The average of a set of numbers is worked out by adding the numbers together and then dividing by the number of numbers. Work out the average of: 1, 1, 1

_______

1, 1, 4

_______

1, 4, 7

_______

4, 7, 13

_______

Describe, in words, a simple pattern that you notice about these answers: _______________________________________ Class 6A go on a Geography trip to Eastbourne and investigate the size of pebbles on the beach. Jonnie picks up seven small pebbles and measures their lengths in millimetres. The lengths of the first six pebbles are: 1, 1, 1, 4, 7, 13 Assuming that the pattern that you observed above continues to hold, work out the length of Jonnie’s seventh pebble. ________ 27.

Tristan is given six bags of fruit. Bag A contains 2 apples, 4 oranges and 3 pears. Bag B contains 3 apples, 1 orange and 2 pears. Bag C contains 4 apples, 5 oranges and 3 pears. Bag D contains 4 apples, 6 oranges and 4 pears. Bag E contains 6 apples, 4 oranges and 3 pears Bag F contains 7 apples, 7 oranges and 7 pears. He is allowed to choose one of these bags and then pick just one piece of fruit from that bag at random. Which bag should he choose if he is to maximise his chance of picking an apple? _________ Which bag should he choose if he is to minimise his chance of picking a pear? _________

SPACE FOR WORKING

Answer 28.

The diagram below shows a sequence of squares drawn on a grid. The coordinates of the centre of square number 1 are (1,1). The coordinates of the centre of square number 2 are (2,3). The first number in the pair is the x-coordinate and the second number is the y-coordinate. Write down the coordinates of the centre of square number 3

___________________

square number 4

___________________

square number 10

___________________

square number 234

___________________

The y-coordinate of the centre of one of the squares in this sequence is 2177. Work out the x-coordinate of this square. ________________ y 6

5

3

4

3

2

2

1

1

1

SPACE FOR WORKING

2

3

4

5

6

x

29. In the triangles shown below each number is the sum of the two numbers directly underneath it. For example, 26 = 12 + 14 and 5 = 1 + 4. 26 12 5 1

14 7

4

7 3

4

Complete the triangle of numbers: ____ ____ ____ 1

____ 8

____

7 ____

5

Complete the triangle of numbers: 101 54 ____ 12

SPACE FOR WORKING

____ ____

____

____ 8

____

Answer 30. The diagram below shows a rectangle, 9 units long, 6 units wide and with parts of non-overlapping circles drawn all over it. The circles all have the same radius and the area of each is 7 square units. Work out the shaded area.

9 units

6 units

Shaded area = _________ square units The diagram below shows a square which is 3 units long with four identical semi-circles drawn on each edge. These semi-circles overlap to create four petals which are shaded on the diagram. The area of each semi-circle is 3.5 square units. Work out the shaded area.

3 units

Shaded area =

________ square units

SPACE FOR WORKING

GO BACK AND CHECK YOUR ANSWERS CAREFULLY

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